Finite Group DatabasebetaFinite Group DatabasebetaOrder 35072.
910 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 910 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C137 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3568×C137 | C2 | semidirect |
| 2. #3217×C137 | C2 | semidirect |
| 3. #1657×C137 | C2 | semidirect |
| 4. #1655×C137 | C2 | semidirect |
| 5. #1535×C137 | C2 | semidirect |
| 6. #563×C137 | C22 | semidirect |
| 7. H(3,𝔽4)×C137 | C22 | semidirect |
| 12. C2×#127×C137 | C22 | semidirect |
| 15. #490×C137 | C22 | semidirect |
| 20. #432×C137 | C22 | semidirect |
| 21. #330×C137 | C22 | semidirect |
| 22. #329×C137 | C22 | semidirect |
| 141. #19094 | C137 | direct (N × H) |
| 142. C137 | #19094 | direct (N × H) |
| 143. #3568 | C2×C137 | semidirect |
| 144. #3217 | C2×C137 | semidirect |
| 145. #1657 | C2×C137 | semidirect |
| 146. #1655 | C2×C137 | semidirect |
| 147. #1535 | C2×C137 | semidirect |
| 148. #563 | C22×C137 | semidirect |
| 149. H(3,𝔽4) | C22×C137 | semidirect |
| 154. C2×#127 | C22×C137 | semidirect |
| 157. #490 | C22×C137 | semidirect |
| 162. #432 | C22×C137 | semidirect |
| 163. #330 | C22×C137 | semidirect |
| 164. #329 | C22×C137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3568×C137 | 2 |
| #3217×C137 | 2 |
| #1657×C137 | 2 |
| #1655×C137 | 2 |
| #1535×C137 | 2 |
| #19094 | 137 |